Other studies presented small numbers of FGs candidates [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, whereas the first large sample of FG candidates was presented in [7]}: in this work, the authors selected 34 galaxy aggregations obtained from the Sloan Digital Sky Survey Data Release 5 [8]} by cross matching the sample of SDSS Luminous Red Galaxies [9]} with sources in the ROSAT all-sky bright source catalogue [10]}. The result of the cross match was a list of elliptical galaxies surrounded by an X-ray halo. Then, the magnitude gap was computed within a fixed radius (500 kpc) and in a fixed redshift range (\(\Delta z = 0.002\)  when spectroscopic redshift is available, \(\Delta z = 0.035\)  when only photometric redshift is known). These 34 FG candidates were then studied in detail by the Fossil Group Origins (FOGO) project [11]}. This observational project produced a set of results analysing the properties of these systems. In the framework of this project, [12]} confirmed that \(15^{+8}_{-5}\)  of the candidates are FGs according to the [13]} or [14]} definitions. The uncertainties in the number of confirmed FGs reflect those on the definition of \(r_{200}\) .
The large difference between the proposed candidates and the confirmed fossils can be explained with a stricter implementation of the definition criteria (e.g. differences in the search radius and membership definition). From the comparison between [7]} and [12]} it seems clear that three types of observations are needed in order to strictly define an FG: (i) X-ray data, required to estimate the mass of the system and define the virial radius, (ii) multi-object spectroscopy, in order to identify the real members of the FG, removing fore- and background objects, and (iii) an optical image, needed to measure the magnitude of each galaxy and to compute the magnitude gap between the brightest galaxy and the other members. The combination of the strong observational effort together with the demanding observational definition is probably the main limit for the building of a large and homogeneous dataset of fossil systems.
However, the number of known FGs kept growing in the last decade. Without intending to be exhaustive, [17]} used SDSS-DR4 and ROSAT to build a sample of 25 FG candidates, [18]} found 109 FGs obtained from SDSS-DR7 using a friend-of-friend algorithm, [19]} presented a catalogue of 395 nearby groups and claimed that \(\sim 25\%\)  of those are FGs, [20]} presented a sample of 17 FG candidates, and [21]} presented a catalogue of 129 groups, of which 22 \(\pm 6\%\)  are fossils.
While the number of candidates is rising, it become more and more complicated to have dedicated multi-object spectroscopic observations to constraint membership. The main drawback of this strategy is that the purity of the sample is difficult to control and non-fossil systems can dilute the statistical relevance of the results.
It is thus complicated to estimate the number of “genuine” FGs, namely those that strictly accomplish the operational definitions, known up to date. However, in the last section of this review we will try to define a sample of such genuine systems.
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